Kindle development is Java. xword is C code. I'm not saying it's impossible, but it's not necessarily easy either.
And yes, .puz files are trivially small -- I just downloaded the free classic NYTimes puzzle and it was 1.84 KB.
However according to
https://kindlepublishing.amazon.com/...epubs/kdk/home, apps have a maximum limit of 100KB/user/month.
So, an app ought to be able to load about 50 puzzles/mo before you hit the limit. Ok for the casual solver, perhaps. Not so good if you're working the NYT daily and also like to do other puzzles too.